INVARIANCE THEOREMS FOR A CLASS OF SYSTEMS OF RANDOM NONLINEAR EQUATIONS OVER AN ARBITRARY FINITE RING WITH LEFT UNITY

被引：2

作者：

Levitskaya, A. A. ^{[1
]}

机构：

[1] Natl Acad Sci Ukraine, VM Glushkov Inst Cybernet, Kiev, Ukraine

来源：

CYBERNETICS AND SYSTEMS ANALYSIS | 2008年 / 44卷 / 06期

关键词：

system of random nonlinear (linear) equations over a finite ring with left unity (over a finite field); factorial moment of the number of nonzero solutions of a system; distribution of the number of nonzero solutions of a system;

D O I：

10.1007/s10559-008-9066-0

中图分类号：

TP3 [计算技术、计算机技术];

学科分类号：

0812 ;

摘要：

A class of homogenous systems of random nonlinear equations over an arbitrary finite ring with left unity is considered. The author analyzes the invariance boundaries for limit factorial moments of nonzero solutions, the limit distribution of the number of nonzero solutions, and the geometrical structure of the set of nonzero solutions of the system as the number of unknowns tends to infinity.

引用

页码：884 / 891

页数：8

共 19 条

[1] Invariance theorems for a class of nonlinear systems of equations over an arbitrary finite field
Levitskaya, AA
[J]. CYBERNETICS AND SYSTEMS ANALYSIS, 1996, 32 (02) : 239 - 247
[2] INVARIANCE THEOREMS FOR A SYSTEM OF RANDOM LINEAR-EQUATIONS OVER AN ARBITRARY FINITE RING
LEVITSKAIA, AA
[J]. DOKLADY AKADEMII NAUK SSSR, 1982, 263 (02): : 289 - 291
[3] INVARIANCE THEOREMS FOR A SYSTEM OF RANDOM LINEAR-EQUATIONS OVER A FINITE RING WITHOUT THE LEFT IDENTITY
LOVITSKAYA, AA
[J]. DOPOVIDI AKADEMII NAUK UKRAINSKOI RSR SERIYA A-FIZIKO-MATEMATICHNI TA TECHNICHNI NAUKI, 1984, (09): : 70 - 71
[4] SOLVING THE PROBLEM OF INVARIANCE OF PROBABILISTIC CHARACTERISTICS FOR A PRIORI SOLVABLE SYSTEMS OF RANDOM NONLINEAR EQUATIONS OVER A FINITE COMMUTATIVE RING WITH UNITY
Levitskaja, A. A.
[J]. CYBERNETICS AND SYSTEMS ANALYSIS, 2010, 46 (03) : 363 - 375
[5] THE PROBABILITY OF CONSISTENCY OF A SYSTEM OF RANDOM LINEAR-EQUATIONS OVER AN ARBITRARY FINITE RING
LEVITSKAYA, AA
[J]. THEORY OF PROBABILITY AND ITS APPLICATIONS, 1986, 30 (02) : 364 - 375
[6] Systems of random equations over finite algebraic structures
Levitskaya A.A.
[J]. Cybernetics and Systems Analysis, 2005, 41 (1) : 67 - 93
[7] On non-linearity and affine equivalence of permutations over an arbitrary finite commutative ring with unity
Mishra, P. R.
Kumar, Yogesh
Pillai, N. R.
Sharma, R. K.
[J]. CRYPTOLOGIA, 2018, 42 (01) : 81 - 94
[8] Characteristics of random systems of linear equations over a finite field
Shapovalov, A. V.
[J]. DISCRETE MATHEMATICS AND APPLICATIONS, 2008, 18 (06): : 569 - 580
[9] LIMIT BEHAVIOR OF NUMBER OF SOLUTIONS TO SYSTEM OF ARBITRARY LINEAR EQUATIONS OVER A FINITE FIELD AND FINITE RING
KOVALENKO, IN
LEVITSKAYA, AA
[J]. DOKLADY AKADEMII NAUK SSSR, 1975, 221 (04): : 778 - 781
[10] Two theorems on estimates for solutions of one class of nonlinear equations in a finite-dimensional space
Koshanov, B. D.
Kakharman, N.
Segizbayeva, R. U.
Sultangaziyeva, Zh. B.
[J]. BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS, 2022, 107 (03): : 70 - 84

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